Question

in randomized, double-blind clinical trials of a new vaccine, infants were randomly divided into two groups. subjects in group 1 received the new vaccine while subjects in group 2 received a control vaccine. after the second dose, 111 of 714 subjects in the experimental group (group 1) experienced fever as a side effect. after the second dose, 68 of 595 of the subjects in the control group (group 2) experienced fever as a side effect. does the evidence suggest that a higher proportion of subjects in group 1 experienced fever as a side effect than subjects in group 2 at the α = 0.05 level of significance?
the samples are independent.
determine the null and alternative hypotheses.
h₀: p₁ = p₂
h₁: p₁ > p₂
find the test statistic for this hypothesis test.
2.16 (round to two decimal places as needed.)
determine the p - value for this hypothesis test.
0.015 (round to three decimal places as needed.)
interpret the p - value.
if the population proportions are one would expect a sample difference proportion the one observed in about out of 1000 repetitions of this experiment (round to the nearest integer as needed.)

Explanation:

Step1: Understand the P - value concept

The P - value is the probability of obtaining a result as extreme or more extreme than the observed result, assuming the null hypothesis ($H_0:p_1 = p_2$) is true.

Step2: Relate P - value to the statement

We are given $P - value=0.015$. To fill in the blanks:
If the population proportions are equal (since the null hypothesis assumes $p_1 = p_2$), one would expect a sample difference proportion greater than or equal to (because the alternative hypothesis is $H_1:p_1>p_2$) the one observed in about $0.015\times1000 = 15$ out of 1000 repetitions of this experiment.

Answer:

If the population proportions are equal one would expect a sample difference proportion greater than or equal to the one observed in about 15 out of 1000 repetitions of this experiment.